Two possiblities come to mind quickly since you've defeated the Drengin/Korath
1) Use the largest fleets you can (by this I don't mean Hull sizes, small Hulls should be fine) and send
several so that you can attack on the same turn befor that ship can repair. Don't put defenses and probably not engines on them either. Just use ALL the space for weapons, if the DL's have a particular defense, and it is sizable on that single ship defending, then certainly use a different weapon type.
The thing here is that your ships fire back even if they are destroyed on the first hit, so eventually, with enough ships you will beat it, if it does not repair.
or you can
2) Fly up the tech tree so that you can better implement plan 1.
It is supposed to be an epic battle against the DL's. That way you get a feel for how superior their race was to the young ones. Get you into the story so to speak